Abstract: A time-varying t-copula model is used to investigate the dependence between return series of Dow Jones Industrial Average Index and S&P 500INDEX.The difficulty of time-varying t-copula model is how to specify evolution equation of time-varying dependence parameters.A new evolution equation have been established to describe time-varying parameters including time-varying related correlation coefficient and degree of freedom.Moreover,stimulated portfolio return series is generated by monte-carlo method in order to get VaR of different portfolios.Next,a simple analysis on the risk trend of these portfolios is given here.The VaR results are tested by backtesting method,the result of these tests shows that VaR series calculated by time-varying copula model have a good coverage rate to factual lost.

Key words: time-varying, Copula, VaR